Paternity Index Calculator: Likelihood Ratio & Probability of Paternity

simulator advanced ~12 min
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W = 99.9999% — paternity practically proven

With 16 loci averaging PI of 2.5, the combined paternity index exceeds 2.3 million, yielding a probability of paternity of 99.9999% assuming equal prior odds.

Formula

Per-locus PI: PI_i = P(child genotype | alleged father is father) / P(child genotype | random man is father)
Combined PI: CPI = ∏ PI_i across all tested loci
Probability of paternity: W = (CPI × prior) / (CPI × prior + (1 - prior))

The Likelihood Ratio Framework

Paternity testing frames identity as a hypothesis test. The prosecution hypothesis H1 states the alleged father is the true biological father; the defense hypothesis H2 states a random unrelated man from the population is the father. At each STR locus, the likelihood ratio quantifies how much more probable the observed child-mother-alleged father genotype trio is under H1 versus H2.

Combining Evidence Across Loci

Because STR loci on different chromosomes segregate independently, per-locus paternity indices multiply to form the Combined Paternity Index. Sixteen loci with modest individual PIs of 2-3 each produce a CPI in the millions, translating to probabilities of paternity exceeding 99.9999%. This exponential accumulation of evidence is the statistical engine of kinship testing.

Mutation Considerations

STR loci mutate at measurable rates, typically 0.1-0.6% per generation. A true father-child pair may show a one-repeat mismatch at a single locus due to germline mutation. Modern laboratories never exclude on a single mismatch; instead they calculate a mutation-adjusted PI using the known mutation rate, which reduces but does not eliminate the evidence at that locus.

Legal Standards and Reporting

Courts worldwide have adopted the PI/W framework with varying thresholds. The AABB requires testing at a minimum of 15 loci and reporting both the CPI and the posterior probability. The ISFG recommends transparent reporting of assumptions including population databases used, mutation models applied, and prior probability chosen.

FAQ

What is a paternity index?

The Paternity Index (PI) is a likelihood ratio comparing two hypotheses: the tested man is the biological father vs. a random unrelated man is the father. For each STR locus, PI = X/Y where X is the probability of the child's genotype given the alleged father, and Y is the probability given a random man. The combined PI is the product across all loci.

What probability of paternity is considered proof?

Most jurisdictions and the American Association of Blood Banks consider W > 99.0% as 'highly likely' and W > 99.9% as 'practically proven'. With modern 16-24 locus kits, true fathers typically achieve W > 99.9999%.

How do mutations affect paternity testing?

STR loci mutate at rates of 0.1-0.6% per generation. A single-locus mismatch between father and child may be a mutation rather than an exclusion. Labs use mutation-adjusted likelihood ratios and require mismatches at 3+ loci before excluding paternity.

What is the prior probability in paternity testing?

The prior probability represents the pre-test belief that the man is the father, based on non-genetic evidence. Laboratories typically use 0.5 (equal odds) as a neutral prior, though Bayesian analysis allows courts to incorporate case-specific information.

Sources

Embed

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